Asymptotics for Pillai's problem with polynomials
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866908391876591616 |
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| author | Heintze, Sebastian |
| author_facet | Heintze, Sebastian |
| contents | Let $ a_1(x)p_1(x)^n + \cdots + a_k(x)p_k(x)^n $ as well as $ b_1(x)q_1(x)^m + \cdots + b_l(x) q_l(x)^m $ be two polynomial power sums where the complex polynomials $ p_i(x) $ and $ q_j(x) $ are all non-constant. Then in the present paper we will give an asymptotic for the number of pairs $ (n,m) \in \mathbb{N}^2 $ such that the degree of the sum of these two power sums is between $ 0 $ and $ d $ when $ d $ goes to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_07367 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Asymptotics for Pillai's problem with polynomials Heintze, Sebastian Number Theory Let $ a_1(x)p_1(x)^n + \cdots + a_k(x)p_k(x)^n $ as well as $ b_1(x)q_1(x)^m + \cdots + b_l(x) q_l(x)^m $ be two polynomial power sums where the complex polynomials $ p_i(x) $ and $ q_j(x) $ are all non-constant. Then in the present paper we will give an asymptotic for the number of pairs $ (n,m) \in \mathbb{N}^2 $ such that the degree of the sum of these two power sums is between $ 0 $ and $ d $ when $ d $ goes to infinity. |
| title | Asymptotics for Pillai's problem with polynomials |
| topic | Number Theory |
| url | https://arxiv.org/abs/2112.07367 |